28 Electric power – problems and solutions
1. Calculate the electric current of a 10 Watt lamp designed for 12 Volt.
Known :
Power (P) = 10 Watt
Voltage (V) = 220 Volt
Wanted : Electric current
Solution :
Lamp power = 10 Watt = 10 Joule/second
The equation below shows the relation between the electric power (P), electric potential (V) and electric current (I) stated in formula below :
P = V I
Electric current :
I = P / V = 10 / 220 = 1/22 = 0.045 Ampere
2. Calculate the electric power according to the electric circuit below.
Known :
Resistor 1 (R1) = 6 Ω
Resistor 2 (R2) = 6 Ω
Electric voltage (V) = 24 Volt
Wanted : Electric power
Solution :
Equivalent resistor :
R1 and R2 are connected in series. The equivalent resistor :
R = R1 + R2 = 6 Ω + 6 Ω = 12 Ω
The electric current :
I = V/R = 24/12 = 2 Ampere
Electric power :
P = V I = (24)(2) = 48 Watt = 48 Joule/second
3. Calculate the electric current of a 3 kiloWatt designed for 150 Volt.
Known :
Electric power (P) = 3 kiloWatt = 3000 Watt
Electric voltage (V) = 150 Volt
Wanted : Electric current (I)
Solution :
Relation of the electric power (P), electric potential (V) and electric current (I) stated in formula below :
P = V I
The electric current :
I = P / V
I = 3000 Watt / 150 Volt
I = 20 Ampere
4. Calculate the power for a \(10\,\Omega\) resistor with a \(5\,A\) current.
Solution: \( P = I^2 R = 5^2 \times 10 = 250\,W \)
5. Determine the power for a circuit with \(12\,V\) and \(4\,\Omega\) resistance.
Solution: \( P = \frac{V^2}{R} = \frac{12^2}{4} = 36\,W \)
6. A \(60\,W\) bulb operates for \(3\,h\). Calculate the energy consumed.
Solution: \( E = Pt = 60 \times 3 = 180\,Wh = 0.18\,kWh \)
7. Calculate the current for a \(200\,W\) appliance on a \(100\,V\) supply.
Solution: \( I = \frac{P}{V} = \frac{200}{100} = 2\,A \)
8. Find the resistance of a heater that uses \(1200\,W\) at \(240\,V\).
Solution: \( R = \frac{V^2}{P} = \frac{240^2}{1200} = 48\,\Omega \)
9. A \(9\,V\) battery is connected to a \(3\,\Omega\) resistor. Find the power dissipated.
Solution: \( P = \frac{V^2}{R} = \frac{9^2}{3} = 27\,W \)
10. Calculate the power in a \(10\,\Omega\) resistor with a \(100\,V\) supply.
Solution: \( P = \frac{V^2}{R} = \frac{100^2}{10} = 1000\,W \)
11. Determine the voltage required to dissipate \(50\,W\) in a \(10\,\Omega\) resistor.
Solution: \( V = \sqrt{PR} = \sqrt{50 \times 10} = 22.36\,V \)
12. A motor uses \(1500\,W\) and runs for \(4\,h\). Find the energy consumed.
Solution: \( E = Pt = 1500 \times 4 = 6000\,Wh = 6\,kWh \)
13. Find the current of a \(240\,V\) supply if the power is \(1200\,W\).
Solution: \( I = \frac{P}{V} = \frac{1200}{240} = 5\,A \)
14. Calculate the resistance for a \(100\,W\) bulb operating at \(200\,V\).
Solution: \( R = \frac{V^2}{P} = \frac{200^2}{100} = 400\,\Omega \)
15. Determine the power in a \(3\,A\) circuit with a \(15\,\Omega\) resistor.
Solution: \( P = I^2 R = 3^2 \times 15 = 135\,W \)
16. Calculate the voltage needed to dissipate \(100\,W\) in a \(20\,\Omega\) resistor.
Solution: \( V = \sqrt{PR} = \sqrt{100 \times 20} = 44.72\,V \)
17. Find the energy consumed by a \(300\,W\) fan running for \(2\,h\).
Solution: \( E = Pt = 300 \times 2 = 600\,Wh = 0.6\,kWh \)
18. Calculate the current in a circuit with \(1000\,W\) power and \(250\,V\) voltage.
Solution: \( I = \frac{P}{V} = \frac{1000}{250} = 4\,A \)
19. Determine the resistance of a \(400\,W\) toaster operating at \(100\,V\).
Solution: \( R = \frac{V^2}{P} = \frac{100^2}{400} = 25\,\Omega \)
20. Find the power for a \(20\,V\) voltage across a \(5\,\Omega\) resistor.
Solution: \( P = \frac{V^2}{R} = \frac{20^2}{5} = 80\,W \)
21. Calculate the voltage needed to provide \(200\,W\) to a \(25\,\Omega\) resistor.
Solution: \( V = \sqrt{PR} = \sqrt{200 \times 25} = 50\,V \)
22. Determine the energy consumed by a \(500\,W\) machine running for \(5\,h\).
Solution: \( E = Pt = 500 \times 5 = 2500\,Wh = 2.5\,kWh \)
23. Find the current for a \(60\,W\) bulb operating at \(120\,V\).
Solution: \( I = \frac{P}{V} = \frac{60}{120} = 0.5\,A \)
24. Calculate the resistance for a \(40\,W\) lamp running at \(20\,V\).
Solution: \( R = \frac{V^2}{P} = \frac{20^2}{40} = 10\,\Omega \)
25. Determine the power in a \(5\,A\) circuit with a \(12\,\Omega\) resistor.
Solution: \( P = I^2 R = 5^2 \times 12 = 300\,W \)
26. Calculate the voltage required to deliver \(150\,W\) to a \(15\,\Omega\) resistor.
Solution: \( V = \sqrt{PR} = \sqrt{150 \times 15} = 61.24\,V \)
27. Find the energy consumed by a \(800\,W\) air conditioner running for \(3\,h\).
Solution: \( E = Pt = 800 \times 3 = 2400\,Wh = 2.4\,kWh \)
28. Determine the current in a circuit with \(500\,W\) power and \(125\,V\) voltage.
Solution: \( I = \frac{P}{V} = \frac{500}{125} = 4\,A \)
